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[quote=pettifogger][quote=Anonymous][quote=Anonymous][quote=Anonymous]My kid is in first grade and we are working through a calculus textbook at home.  Math just comes to him.  Would love for him to get a better foundation than I can provide.  These college classes sound expensive though.  What is the cost?[/quote]

I have seen claims like this before on DCUM and it blows my mind. I don't think this is actually possible, but I could be wrong! I don't know enough about giftedness. Can you elaborate on how your child has the knowledge and cognitive foundation for calculus at age 6/7?

In terms of your q, if your child is that intelligent, not sure they need to go to college to learn anything. Stick with textbooks and tutors? Or see if DC can audit? There's also MOOCs, which could be a lot better than any inperson instruction where you are at the mercy of who ever gets assigned to teach the course (whereas MOOCs often have amazing teachers). DC must also be able to use a computer by now.[/quote]

Kid is 6yo and uses computers.  He was reading chapter books during K so we focused on math over the summer.  Algebra, geometry, trigonometry, etc.  I’m not saying he has mastered anything but we are working through a calculus textbook now to keep him interested.  I’m really confused what to do about school so I do appreciate the suggestions.  I was initially considering college courses as an option a few years from now, but he also deserves a childhood and likes playing with kids his age.  We are private people and don’t want any attention.[/quote]
Teach him the exciting topics of math that students don't get to see in K12. Teach him a little number theory, teach him how to count things, i.e a little combinatorics, introduce probability through games and puzzles. Perhaps give him some interesting problems found from the many math contests out there, e.g Mathcounts at the middle school level has plenty of interesting problems, there's the AMC 8, as well as other various contests. These problems will be exciting for him, and it will give him an opportunity to engage, play, and master the material. It's fine to talk to him about calculus when he's curious and asks for it, but if you want him to enjoy his childhood and have a gifted education, trying to teach him the mechanics of calculus is not really the best idea given how many other exciting mathematical topics are out there. Pick up a math circle book (for example Mathematical Circle Diaries, or any of the other books from the AMS Mathematical Circles library) and work together with him through the many exciting problems. Do lots of puzzle and logic problems to develop his analytical skills. Play chess and other logic and strategy games, teach a bit of programming -- Python is a good one to start as it is very syntax friendly. Challenge him to build an interesting program or toy game so he can actually learn programming skills in a fun way.

Most importantly, be attuned to his [i]changing interests[/i]; if he latches onto math contest problems and wants more, great! Or if he just likes reading a math book on his own that's also great! If you find you don't have enough time or ability to devote to developing his education yourself, look to some summer programs for gifted kids to supplement. But if he is truly advanced compared to others his age he may get very bored, so you will have to very careful as to what programs to pick for him.[/quote]

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